Of Harbingers and Higher Modes: Improved gravitational-wave early-warning of compact binary mergers

A crucial component to maximizing the science gain from the multi-messenger follow-up of gravitational-wave (GW) signals from compact binary mergers is the prompt discovery of the electromagnetic counterpart. Ideally, the GW detection and localization must be reported early enough to allow for telescopes to slew to the location of the GW-event before the onset of the counterpart. However, the time available for early warning is limited by the short duration spent by the dominant ($\ell = m = 2$) mode within the detector's frequency band, before the binary merges. This can be circumvented if one could exploit the fact that GWs also contain contributions from higher modes that oscillate at higher harmonics of the orbital frequency, which enter the detector band well before the dominant mode. In this letter, we show that these higher modes, although smaller in amplitude, will enable us to significantly improve the early warning time for compact binaries with asymmetric masses (such as neutron-star-black-hole binaries). We investigate the gain in the early-warning time when the $\ell = m = 3$ and $\ell = m = 4$ modes are included in addition to the dominant mode. This is done by using a fiducial threshold of 1000 sq. deg. on the localization sky-area for electromagnetic follow-ups. We find that, in LIGO's projected "O5-like" network of five GW detectors, for neutron-star-black-hole mergers expected to produce counterparts, we get early-warning gains of up to $\sim 25$ s, assuming the source at a distance of $40$ Mpc. These gains increase to $\sim 40$ s in the same five-detector network with three LIGO detectors upgraded to "Voyager" sensitivity, and $\sim 5$ min. in a third-generation network when the source is placed at $100$ Mpc.